Computer locking up after random lengths of time

So I had this happen a few times, and more recently every day. I recently reinstalled windows 7 x64 to clean everything up, but unfortunately the problem persists.

After a certain amount of time, whatever window I am on becomes unresponsive. Following that if I try to use other windows, they too become unresponsive. task manager won't come up during this time, the computer is just 1 window/application at a time locking up to the point where I can do nothing except power it down by holding the power button and restarting.

It is also very slow starting up and seems to be slow at times during use. Sometimes when I start it up or when I am doing something at the same time (like deleting files for instance). I have 12 gb of RAM and when I am monitoring the performance the computer hardly goes about 20% usage and still seems slow.

I wasn't sure if it was a RAM problem or if it was even hardware at all, could it be software?

Thanks for the help.

Please fill out your system specs, use Speccy in my sig. Do you have background programs running? Do you have a clean boot? Have you tested your memory and hard drive?